Problem preview

S-ID.4 Warmup M3-053-A06-V02

Use mean and standard deviation to fit normal distributions and estimate population percentages with technology.

Compute a normal area to four decimals

Problem

For \(X~~N(100,~10)\), compute \(P(X~>~90)\). Give the \(\operatorname{normalcdf}\) setup, decimal probability, and percent interpretation.

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normalcdf(90, infinity, 100, 10) = 0.1587, so about 15.87% of values are above 90.

normalcdf(90, infinity, 100, 10) = 0.8413, so about 84.13% of values are above 90.

normalcdf(-infinity, 90, 100, 10) = 0.1587, so about 15.87% of values are below 90 rather than above it.

normalcdf(90, infinity, 10, 100) is entered with mean and standard deviation reversed; claiming 0.8413 from this setup does not find the requested probability.

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Curriculum context

Course: Math III
Standard: S-ID.4
Category: Statistics and Probability
Domain: Interpreting Categorical and Quantitative Data
Objective: Use mean and standard deviation to fit normal distributions and estimate population percentages with technology.
Problem type: Compute a normal area to four decimals